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To compare the precedence of two methods, their parameter specializers are examined in order. The default examination order is from left to right, but an alternative order may be specified by the :argument-precedence-order option to defgeneric or to any of the other operators that specify generic function options.
The corresponding parameter specializers from each method are compared. When a pair of parameter specializers agree, the next pair are compared for agreement. If all corresponding parameter specializers agree, the two methods must have different qualifiers; in this case, either method can be selected to precede the other. For information about agreement, see Agreement on Parameter Specializers and Qualifiers.
If some corresponding parameter specializers do not agree, the first pair of parameter specializers that do not agree determines the precedence. If both parameter specializers are classes, the more specific of the two methods is the method whose parameter specializer appears earlier in the class precedence list of the corresponding argument. Because of the way in which the set of applicable methods is chosen, the parameter specializers are guaranteed to be present in the class precedence list of the class of the argument.
If just one of a pair of corresponding parameter specializers is (eql object), the method with that parameter specializer precedes the other method. If both parameter specializers are eql expressions, the specializers must agree (otherwise the two methods would not both have been applicable to this argument).
The resulting list of applicable methods has the most specific method first and the least specific method last.